Regularity in Weighted Graphs: A Symmetric Function Approach

2015/07/17 by Marni Mishna, Mishna, Marni
Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1507.05121

9 pages

arxiv created 2015/07/17 · openalex publication_date 2015/07/17 · arxiv updated 2015/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we consider k-regular multigraphs, where the possible edge multiplicities are controlled. These structures are considered in a question recently posed by Brendan McKay. We express the generating functions using the scalar product of symmetric functions, and consequently give conditions on when the classes are D-finite. We appeal to symmetric species results of Mendez to write the expressions in a systematic way.

Related

• Weighted Regularity Lemma with Applications
• Chromatic MacMahon symmetric functions of graphs
• Symmetric function generalizations of graph polynomials
• Regular partitions of gentle graphs
• Counting induced subgraphs with the Kromatic symmetric function